The UCAC2 catalog includes a proper motion measurement,
though it is only marginally significant,
about 1.5 times the uncertainty.
Using the proper motion,
I computed the star's position
on June 12, 2006, or epoch 2006.444:

RA = 265.3003098 = 17:41:12.07435
Dec = -15.6929373 = -15:41:34.574

The magnitude of the star is not measured very well;
the USNO B1.0 lists B=15.6 and R=14.0.
We might guess the star to have V=14.8 or so.

which lists its visual magnitude as 13.8.
We therefore expect that the combined
light of the system should be about
1.4 times brighter than Pluto alone, or about 3.5
times brighter than the star alone.
While the star is completely hidden by Pluto,
the combined light should drop by
about a factor of 40 percent, or about 0.36 magnitudes.

According to the JPL ephemeris,
Pluto's motion is 3.95 arcseconds per hour,
or 0.001097 arcseconds per second.
At a distance of 30.12 AU from Earth,
Pluto's apparent angular diameter
is (according to the JPL ephemeris) 0.109 arcseconds;
but that doesn't agree with this calculation:
given a radius of Pluto of R = 1137 +/- 8 km
(from Elliot et al., Nature 424, 165, 2003),
and a distance of 30.12 AU, I find
the apparent angular diameter of Pluto should be
0.1041 arcsec.
I'll adopt this smaller value from this point on.
If the center of the planet were to
pass directly over the star,
the occultation would last about
95 seconds.

25cm Newtonian on GEM (homemade)
Meade Deep Sky Imager Pro
Exposure time 1 second
Time - I synced my PC to my GPS timer before observing. The time in the
'Properties' is accurate to 0.25 second, however it is in local time.
ie... 13 June 2006, 2:25:18 AM = 12th June 16:25:18UT

Dave processed his raw video frames,
subtracting a dark frame and dividing by
a flatfield.
He kindly sent the processed frames to me.

I had to convert the images
from 32-bit floating-point FITS format
into 16-bit integer FITS format
to handle them, but that conversion
did not incur any penalty:
the original pixel values were integers,
ranging from roughly 3200 counts to 6500 counts.

I have oriented the image so that it matches the
standard astronomical chart, with North up and East
to the left.
For future reference, I selected a small number of
stars, ranging from some the brightest in
the frame to some a bit fainter than the target.
In the chart below, the circled object without
a label at the center of the frame
is the combined light of Pluto and the star.

found all stars with peak pixel values
more than 3 times the sky-sigma above the sky

measured the instrumental magnitude of all
stars using circular apertures of radius
3, 4, 5 pixels,
and a sky annulus of radii 10 and 20 pixels

There were typically 200 stars detected in each frame.

After finding stars in 333 frames,
I used the
ensemble package
to perform
"inhomogeneous ensemble photometry"
on the entire set.
In effect, I used about 200 stars to define
a mean light level for 333 frames,
making small adjustments to each frame to bring
it into best agreement with the average.

The end result is a set of "mean" magnitudes
for each star, with associated standard deviation.
A "sigma-versus-magnitude" plot for the ensemble shows
the usual form: small scatter at the bright end,
larger scatter at the faint end.
Below is the plot for the measurements made
through an aperture of radius 3 pixels:

Outliers on this plot are objects which vary more
than most of their peers.
The combined Pluto-plus-star object
is the outlier at differential magnitude 2.5,
with scatter 0.133 magnitudes.
(The big outlier at differntial magnitude 1.9 is
due to a cosmic ray and/or blend of two stars, I think)

Since the 3-pixel aperture provided the smallest
scatter for faintish stars, I decided to use
the 3-pixel aperture results for further work.

Here are sample light curves for the objects marked
in the charts above:

As you can see, most of the objects have roughly
constant brightness throughout the video record.
The brighter objects have smaller scatter around
their mean values.
The magenta squares, star C, show a definite drop
in brightness of about 0.10 mag at about
the halfway point of the record;
I suspect this is due to the star drifting into
a dust donut which appears on the image.

The combined light of "Pluto-plus-star" is shown as
the green crosses.
Clearly, Dave recorded the occultation.

Was this occultation central? That is, did
the star pass directly behind the center of the
disk of Pluto?
There are two ways we can address this question.

First, we can use the best position of the star,
and a recent ephemeris of Pluto, to predict the
geometry of the event.
Using the position of the star from the UCAC2, with
proper motion as provided in that catalog,
and using the ephemeris of Pluto provided by
the JPL Horizons system (from a query made
on June 29, 2006),
I made the following graphs showing Pluto's
motion relative to the star.
First, a "wide-field" view, spanning 2 arcseconds:

A closeup shows more clearly that Pluto's center
misses the star by a significant fraction of
its radius:

Let's use the letter b to
denote the angular separation between Pluto's center and
the star at closest approach; this is the standard
in discussions of this "impact parameter."
Look at the left-hand position on the figure below.

As a side note, it looks to me as if this
prediction is not completely consistent with
the figure of the shadow falling on the Earth,
shown near the top of this document.
Dave's location, if I read my maps correctly,
should be close to the red star on the eastern
coast of Australia, which lies outside the
dark grey track of the planet's shadow.
Hmmm.

But please note that the exact location of the
star is not known. The proper motion between
2000 and 2006, for example, is about 17 milliarcseconds,
but with a formal uncertainty of about 11 milliarcseconds.
On the scale of the chart above, each square of
the dotted grid is 50 milliarcseconds
on a side, and the distance between the
southern limb of Pluto and the plotted track
of the star is about 16 milliarcseconds.

Now, another way to derive the offset between the
track of Pluto's center and the star is to measure
the duration of the occultation.
My photometry suggests that the drop in
light starts at frame index 145 and ends
at frame index 198; the duration of the event
is thus 53 frames.
The prediction for a central occultation,
on the other hand, is 94.9 seconds.

The original text here was:
"or, at an average cadence of 1.4 seconds
per frame, 71 frames."
However, this cadence is incorrect, so the main text
now has the proper numbers.

Dave's sequence of 333 frames starts at UT 16:17:34
and ends at 16:28:39. That's a duration of 665 seconds.
The separation between each pair of successive frames
is (665 sec) / (332 intervals) = 2.003 seconds
per interval.
Thus, we can use a cadence of 1 image every 2.003 seconds.
We expect that a central occultation
of 94.9 seconds should take (94.9 sec) / (2.003 sec/frame) = 47.4
frames.

Wait a minute! How can the light dim for
53 frames if even a perfectly central
pass behind Pluto should require only 47 frames?
The answer is (very probably) Pluto's atmosphere:
previous occultations have revealed that the
atmosphere is dense enough to produce measureable
extinction at heights of 50-60 km above the surface.
That increases the apparent diameter
of Pluto-plus-atmosphere to about 1250 km,
which translates into an apparent angular diameter
of 0.1144 arcseconds.
The duration of a central occultation would
then be

0.1144 arcsec
------------------- = 104.3 seconds
0.001097 arcsec/sec

At the average rate of 2.003 seconds per frame, we
expect a central occultation of Pluto-plus-atmosphere
would take about 52 frames.

The ratio of durations
(see the right-hand position on the figure above)
is

Hmmm. The timing information suggests that
the occultation was very nearly central.
This doesn't agree with my astrometry --
that indicates that Pluto's center passed quite a bit to the side
of the star.
I don't know how to resolve this discrepancy ...

In theory, if a planet with an atmosphere
passes directly in front of a star,
the light curve should show
a central peak in brightness, due to the refraction of
light through the atmosphere of the planet.

Observations of occultations by Pluto
in the past with very high signal-to-noise ratio
have in the past shown small "kinks" in the disappearance
and re-appearance, due to clouds in the atmosphere.
However, the present measurements lack the precision to show
any such features.

Should we expect to see any evidence of diffraction
phenomena in this light curve?
Let's find out.
In a document describing
diffraction effects during a lunar occultation,
we see that the size of fringes projected onto the
Earth during an occultation is

fringe size = sqrt ( L * λ )

where L = 30.12 AU = 4.506E12 m
is the distance between the occulting body (Pluto) and Earth,
and λ = approx 600 nm = 6E-7 m
is the wavelength of the light.
The fringe spacing computed from these values
is about fringe = 1644 m in width.

As Pluto moves in front of the star, the fringes sweep
across the ground. How fast do the fringes move?
The velocity on the ground is given by
properties of the occulting body (Pluto):

Each fringe will sweep past the observer in
(fringe size) / (velocity) = approx 0.07 seconds.
In Dave Gee's video, with exposure times of 1 second,
any fringe effects will be smeared out and invisible.

In order to compare the observations to a model of starlight
being absorbed by the atmosphere of Pluto, it is necessary
to determine the intensity of the background star alone
during the occultation.
Here's my best attempt to do so ...

Ideally, one would use images showing Pluto and the
background star well separated, taken on the same
night as the occultation, to measure the brightness
of each object alone.
The data which Dave sent me did not include any
images taken on June 12 far enough from the time of
occultation to show the two objects separately
(although Dave has indicated that he has such
images).
However, he did send a single image, the sum of
five 4-second exposures, taken 4 nights later.
In this image, the target star and Pluto are
_very_ far apart:

Although this image was taken with the same instrumental
setup as the images on June 12 (according to the FITS
header values),
it differs in a way from the images taken
during the occultation: it covers the same field on
the sky, but has a different aspect ratio:
June 12 images are 508-by-489 pixels,
while the June 16 composite is 648-by-489 pixels.
I couldn't use my standard tools automatically to compare the
photometry of objects in the later image with those
from the night of the occultation;
instead, I had
to pick a small number of stars which appear in both
images and compare their instrumental magnitudes by
hand. Sigh.

The later image is deeper and has a slightly sharper PSF
(2.5-2.8 pix FWHM versus 3.5 pix FWHM)
than the occultation images.
I used a circular aperture of radius 3 pixels to measure
objects on both sets of images.
I tried using two different sets of objects to
determine the instrumental magnitude offset between
the ensemble system (night of occultation) and the
single deep later image:
one was the set of labelled stars shown above,
the other a set of bright stars.
Each set gave me the same magnitude offset
within the uncertainty -- which was about 0.040 mag.

What I found was that, in the magnitude scale
of the ensemble solution,
Pluto alone had a differential magnitude of 2.912 (+/- 0.043)
and the background star 3.825 (+/- 0.048).
The values in parantheses are the formal
uncertainties in the magnitudes,
but I suspect them to be underestimates of the
true uncertainties.
Translating these numbers into a ratio of intensities,
this means that on the night of June 16,
Pluto was 0.913 mag brighter than the background star;
that's a factor of 2.32 times brighter.

Now, there are two ways we can look at the
occultation light curve at this point, as we try
to isolate the light of the star.

assume that the background star's ensemble magnitude
on June 12 was exactly 3.825; in other words,
assume that the brightness of the background star
relative to its neighboring stars was exactly the
same on the two nights. I favor this option.

assume that the ratio of Pluto-to-background_star
was the same on June 16 and June 12.
This requires that Pluto not vary in brightness
itself during the 4 days between the two datasets,
which is probably not true at the level of a few
percent.

The difference between these two methods is small;
if we follow the first method, we find that Pluto had
to be about 3 percent brighter on June 12 than on June 16.
I will follow the first option from this point on.

Now, look at the light curve of the event again:

You can see that the combined light of Pluto-plus-star
seems to decrease very slightly over the course of the
333 frames.
Let's deal with this.

First, I'll convert the measurements from a magnitude scale
to an intensity scale with an arbitrary zero-point.
Using the intensity values, I looked at mean values
during three periods:

The average of the before-event and after-event values
is 10105 counts, with an uncertainty of about 750 counts.
I will not attempt to correct the slight linear
decrease in overall light during the course
of the observations.

Using the ensemble differential magnitude of the background
star from the night of June 16, and converting to the same
linear intensity scale, I find the star has 2951 +/- 127 counts.
That means that
the brightness of Pluto during the occultation must have
been
10105 - 2951 = 7154 counts , with an uncertainty of about 877.

Had I chosen to use the measurement of Pluto's brightness
from the night of June 16 at this point,
I would have ended up with an intensity of 6842 counts for
Pluto alone at this point.
The two methods thus agree within the uncertainties....

Okay. I can now convert the observed occultation
from differential magnitudes to linear intensity,
and then subtract the brightness of Pluto,
to yield a light curve of the background star alone
during the occultation:

Now, note that I almost certainly didn't compute the
contribution of Pluto correctly:
during the central portion of the occultation,
every datum is below zero intensity.
One would expect a set of random fluctuations centered
on zero intensity.
It's likely, therefore, that my method slightly
overestimated the light from Pluto.
However, note that the formal uncertainty in the
value I derived for Pluto's light is +/- 877 counts
on this scale.
The amount by which one must correct my over-subtraction
in order to yield a mean value of zero intensity during
the center of the occultation is somewhat less than
this uncertainty.

Dave Gault sent me additional images: a set of coadded
exposures taken on the same night as the occultation,
but hours before the event.
My job was to use these images -- in which Pluto and the
target star appear as separated objects --
to measure the relative brightness of the two;
I could then more accurately divide the combined light
during the occultation into contributions from Pluto
and from the star alone.
In the end, I could derive a more accurate light curve
of the star alone.

You can see Pluto's motion relative to the stars
during the night of the occultation in some of
the new images Dave sent me.
Below is a sequence of four pictures taken at 2-hour
intervals.

The very earliest images in Dave's observations showed Pluto
most clearly separated from all other objects.
Using the same aperture (radius 3 pixels) and sky annulus
(inner radius 10 pixels, outer radius 20 pixels)
as I used when measuring the occultation images,
I determined the relative magnitudes of Pluto and the target star.

In images taken at UT 11:45, Pluto's light starts to overlap
with that of stars, so one cannot measure its light accurately.

Using these measurements, I derive an average difference
of 0.883 +/- 0.016 magnitudes between Pluto and the target star.
Note that this is a slightly smaller difference than the
0.913 magnitudes I found in an image taken 4 nights later;
however, it is within the estimated uncertainties.

This difference in magnitudes implies a ratio
of intensities: Pluto is 2.255 +/- 0.033 times
brighter than the target star.
In other words, when their light is combined,
Pluto contributes 0.693 of the total intensity
and the star 0.307 of the total intensity.

Now, I went back to my measurements of the combined
light of Pluto-plus-star from the occultation
and re-analyzed them.
As shown in the section above,
I assigned an arbitrary intensity of 10105 counts
to the combined light of Pluto-plus-star,
averaged over periods just before and just
after the occultation.
With the new ratio of intensities, we can
break this total into pieces like so
(I assign a 2 percent uncertainty to each
contribution, based on the scatter
of the relative magnitudes).

This new value of 7001 counts for Pluto
is slightly smaller than the value of 7154 counts
I derived in my first attempt.

I then subtracted this constant light from Pluto from
all the measurements of intensity during the occultation
to make a light curve of the star alone.
Note that it looks exactly like the first version
in the section above, except for a constant shift of all points
upwards by 53 units.